Complex Fractions

A complex fraction is a fraction that contains a fraction. To simplify a complex fraction, you need to multiply every term by the smallest number that will clear all fractions in the numerator and denominator.

Example:

Solution:

All four denominators will divide easily into 12. You must multiply all of the fractions by 12 to get rid of the fractions:

Your problem now looks like this: .

Try a subtraction problem.

Example:

Solution:

Again, multiply all terms by 12. Don’t forget about the 1.

Fractions: The Vocabulary

• The numerator is the number on top of the fraction.
• The denominator is the number on the bottom of the fraction.
• A mixed number contains an integer and a fraction.
• An improper fraction is larger on the top than on the bottom.
• To find the multiplicative inverse, switch around the top and bottom numbers.
• A complex number is a fraction containing fractions.

Fractions: The Rules

To add or subtract two simple fractions:

• Cross-multiply and perform the function on top.
• Multiply across the bottom. Simplify if necessary.

Addition or subtraction of multiple fractions may require common denominators:

• Find the smallest integer the denominators divide into.
• Multiply each numerator by the same number the denominator is multiplied by to get to the common denominator.
• Perform addition or subtraction on top. Use common denominator as the denominator.